Four prototypical flow fields are expressed below in terms of Cartesian coordinates. In these expressions, y is a constant. i) Planar elongation: ii) Uniaxial extension: iii) Biaxial extension: iv) Pure rotation: For each of these flows, determine: v=ixe - jye, +0e₂ v=2jxe - jy e, - ize, v = jxe + jy e, -2jze, v = iye - jxe, +0e₂ a) the rate of strain tensor € = ½ [Vy + Vy²] and b) the deviatoric stress tensor ( = ½ [Vy – Vy7]. - Based only on your answers to parts (a) and (b), determine: c) whether the flow is incompressible (i.e., is V. y = 0?) d) whether the flow is irrotational. (i.e., is V × v = 0 ?)
Four prototypical flow fields are expressed below in terms of Cartesian coordinates. In these expressions, y is a constant. i) Planar elongation: ii) Uniaxial extension: iii) Biaxial extension: iv) Pure rotation: For each of these flows, determine: v=ixe - jye, +0e₂ v=2jxe - jy e, - ize, v = jxe + jy e, -2jze, v = iye - jxe, +0e₂ a) the rate of strain tensor € = ½ [Vy + Vy²] and b) the deviatoric stress tensor ( = ½ [Vy – Vy7]. - Based only on your answers to parts (a) and (b), determine: c) whether the flow is incompressible (i.e., is V. y = 0?) d) whether the flow is irrotational. (i.e., is V × v = 0 ?)
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
Related questions
Question
![Four prototypical flow fields are expressed below in terms of Cartesian coordinates. In these
expressions, y is a constant.
i) Planar elongation:
ii) Uniaxial extension:
iii) Biaxial extension:
iv) Pure rotation:
For each of these flows, determine:
v = jxex - ¡ye, +0e₂
v=2jxex - jy e, - ize₂
v = jxẹx + jy ẹ, - 2jze₂
v = jye - jxe, +0e₂
a) the rate of strain tensor =
e [Vy + Vy¹] and
2
b) the deviatoric stress tensor = [Vy - Vy¹].
Based only on your answers to parts (a) and (b), determine:
c) whether the flow is incompressible (i.e., is V. y = 0?)
d) whether the flow is irrotational. (i.e., is V × v = 0 ?)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0c361b92-5ba5-4cb8-be48-855fd5894535%2F990f64f1-0906-4d4a-8bab-727e852fb71b%2Fqke544p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Four prototypical flow fields are expressed below in terms of Cartesian coordinates. In these
expressions, y is a constant.
i) Planar elongation:
ii) Uniaxial extension:
iii) Biaxial extension:
iv) Pure rotation:
For each of these flows, determine:
v = jxex - ¡ye, +0e₂
v=2jxex - jy e, - ize₂
v = jxẹx + jy ẹ, - 2jze₂
v = jye - jxe, +0e₂
a) the rate of strain tensor =
e [Vy + Vy¹] and
2
b) the deviatoric stress tensor = [Vy - Vy¹].
Based only on your answers to parts (a) and (b), determine:
c) whether the flow is incompressible (i.e., is V. y = 0?)
d) whether the flow is irrotational. (i.e., is V × v = 0 ?)
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
Step 1
Step by step
Solved in 5 steps with 8 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you
![Elements Of Electromagnetics](https://www.bartleby.com/isbn_cover_images/9780190698614/9780190698614_smallCoverImage.gif)
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
![Mechanics of Materials (10th Edition)](https://www.bartleby.com/isbn_cover_images/9780134319650/9780134319650_smallCoverImage.gif)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
![Thermodynamics: An Engineering Approach](https://www.bartleby.com/isbn_cover_images/9781259822674/9781259822674_smallCoverImage.gif)
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
![Elements Of Electromagnetics](https://www.bartleby.com/isbn_cover_images/9780190698614/9780190698614_smallCoverImage.gif)
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
![Mechanics of Materials (10th Edition)](https://www.bartleby.com/isbn_cover_images/9780134319650/9780134319650_smallCoverImage.gif)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
![Thermodynamics: An Engineering Approach](https://www.bartleby.com/isbn_cover_images/9781259822674/9781259822674_smallCoverImage.gif)
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
![Control Systems Engineering](https://www.bartleby.com/isbn_cover_images/9781118170519/9781118170519_smallCoverImage.gif)
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
![Mechanics of Materials (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781337093347/9781337093347_smallCoverImage.gif)
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
![Engineering Mechanics: Statics](https://www.bartleby.com/isbn_cover_images/9781118807330/9781118807330_smallCoverImage.gif)
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY